Author:
Allen Peter,Lozin Vadim,Rao Michaël
Abstract
In this paper, we study the relationship between the number of $n$-vertex graphs in a hereditary class $\cal X$, also known as the speed of the class $\cal X$, and boundedness of the clique-width in this class. We show that if the speed of $\cal X$ is faster than $n!c^n$ for any $c$, then the clique-width of graphs in $\cal X$ is unbounded, while if the speed does not exceed the Bell number $B_n$, then the clique-width is bounded by a constant. The situation in the range between these two extremes is more complicated. This area contains both classes of bounded and unbounded clique-width. Moreover, we show that classes of graphs of unbounded clique-width may have slower speed than classes where the clique-width is bounded.
Publisher
The Electronic Journal of Combinatorics
Subject
Computational Theory and Mathematics,Geometry and Topology,Theoretical Computer Science,Applied Mathematics,Discrete Mathematics and Combinatorics
Cited by
9 articles.
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